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Ivanshal [37]
3 years ago
11

Find the distance between points A and B, located on the opposite shores of a river, if on one of the shores following segments

have been drawn and measured SB=60m, SC=80m, SD=180m and BC∥AD.

Mathematics
1 answer:
Gre4nikov [31]3 years ago
4 0

Answer:

AB=75m

Step-by-step explanation:

In the \Delta SCB and \Delta SDA

\angle S=\angle S\\BC||AD\\\Rightarrow\angle SBC=\angle SAD\\\angle SCB =\angle SDA

By\ AAA\ \Delta\ and\ \Delta SDA\ are\ similar\\\\ \Rightarrow\frac{SC}{SD} =\frac{SB}{SA} \\\\ \frac{80}{180} =\frac{60}{SA}\\\\ SA=60\times\frac{180}{80} \\\\SA=135\\\\AB=SA-SB\\\\=135-60\\\\=75m

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